Modeling and Analysis of the "Analemma Skylight" By Neil Katz Skidmore, Owings & Merrill LLP Digital Design – SOM New York

Deerfield Academy - Koch Center for Science, Math & Technology Deerfield, Massachusetts, completed 2007

Modeling and Analysis of the "Analemma Skylight"

The Analemma Skylight

In a collaborative project with artist James Turrell, our team, working with astronomer Dick Walker (who, unfortunately, did not live to see the completion of this project), designed a skylight which would admit a spot of light into the building for a specified period each day of the year (from 11A.M. to 1 P.M.), and modeled the "analemma," or path that this spot would strike on the curved brick wall pictured at noon each day.

From inside the space, the skylight appears as a circular opening, six inches in diameter. The center of this opening is the "focal point" of the system used to design and model this effect. If we go to the roof of the building, we can see the skylight very differently, as a molded fiberglass form whose top surface is defined by curves representing paths of the sun at particular times of the day (also analemmas, for 11A.M. and 1P.M., defining the right and left edges) and particular dates (the summer and winter solstices, when the sun is highest and lowest in the sky, defining the top and bottom edges).

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Modeling and Analysis of the "Analemma Skylight"

The effect of this shape is that before 11A.M. (all times are "standard" times) the spot of sunlight is blocked by the form of the skylight from coming into the building; at 11A.M. the spot begins to appear on the brick wall on one side of the noon analemma; the spot moves as the sun moves, and at noon it is directly on the analemma which is inscribed in the wall; the spot keeps moving until 1 P.M , when it begins to disappear. In the summer when the sun is high in the sky, the moving spot is low on the wall; in the winter when the sun is low in the sky, the moving spot is high on the wall.

This illustration shows the concept of how the sun's path was used in the design of the skylight. The sun's path is computed specifically for the geographic location on earth of Deerfield.

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Modeling and Analysis of the "Analemma Skylight"

The red curves indicate the paths of the sun during the year for the times: 11:00, 12:00, 13:00. The green curves indicate the paths of the sun for the dates: 21 June and 21 December.

These curves are projected to a plane. The center of the sphere is the center of the circle in the plane of the ceiling of the space. The plane onto which these curves are projected is 37" above the plane of the ceiling, which is the plane of the rooftop surface.

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Modeling and Analysis of the "Analemma Skylight"

The area defined by the 11:00 analemma projection, the 13:00 analemma projection, the 21 June path of the sun and the 21 December path of the sun defines the opening or hole on the roof surfaces.

Theoretically, we can connect the shape defined by the projection described above to the focal point to create a ruled surface which defines the three- dimensional form of the skylight. The focal point, a theoretical "point" having no size or dimension, would not allow light to pass through it, so the surface was offset three inches, creating a six inch hole, and projecting a spot of an appropriate size onto the wall.

Modeling of the skylight was done with AutoCAD and custom tools (developed in Autolisp) with data indicating the sun's location from: http://aa.usno.navy.mil/data/docs/AltAz.php 5

Modeling and Analysis of the "Analemma Skylight"

Parameters in the application which could be varied included: • Times and dates which defined the opening (we initially used a period of much greater than two hours, but the resulting large opening had other architectural and structural issues associated with it) • Geographic location (although this form was modeled specifically for Deerfield Academy, and its precise latitude and longitude, we can create similar models for other locations by varying these values) • Distance between the ceiling and roof planes, and even the locations in space of these planes (although they are typically parallel to each other, they need not be) • Offset distance

At the time that we were modeling the skylight, our office was beginning to use a rapid-prototyping device, an InVision SR 3-D printer from 3D Systems. We used this machine (our first project application on the new machine) to create a scale model of the skylight, which we brought to the site for testing.

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Modeling and Analysis of the "Analemma Skylight"

Because of the size limitation of the 3D printer, we printed the model in two parts.

In addition to modeling the skylight itself, we also analyzed the resulting spot as it was projected onto the curved brick wall. 7

Modeling and Analysis of the "Analemma Skylight"

In this analysis, the circular opening is modeled as a solid disk (in red), and the projected spot of light is shown as a "shadow" of this disk for a collection of dates and times.

In addition to varying the parameters of the skylight, we can also vary the wall onto which the spot is projected.

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